Effects of nutrient depletion on tissue growth in a tissue engineering scaffold pore

In a tissue engineering scaffold pore lined with cells, nutrient-rich culture medium flows through the scaffold and the cells proliferate. In this process, both environmental factors-such as flow rate and shear stress-as well as cell properties have significant effects on tissue growth. Recent studies have focused on the effects of scaffold pore geometry on tissue growth, while in this work, we focus on the nutrient depletion and consumption rate by the cells, which cause a change in the nutrient concentration of the feed and influence the growth of cells lined downstream. In this paper, our objectives are threefold: (i) design a mathematical model for the cell proliferation describing fluid dynamics, nutrient concentration, and tissue growth; (ii) solve the models and then simulate the tissue proliferation process; (iii) design a "reverse algorithm" to find the initial configuration of the scaffold with the knowledge of the desired property of the final tissue geometry. Our model reduces the numerical burdens and captures the experimental observations from the literature. In addition, it provides an efficient algorithm to simulate the cell proliferation and determine the design of a tissue engineering scaffold given a desired tissue profile outcome.